Secure Coding Over Networks Against Noncooperative Eavesdropping

This paper studies the problem of secure communication over a noiseless network from an information-theoretic perspective. A single-source single-sink acyclic planar network is considered, and the communication between the source and the sink is subject to noncooperative eavesdropping on each link. Using equivocation to measure the confidentiality of messages, we establish sufficient conditions, in terms of communication rates and network parameters, for provably secure communication. A constructive proof, which combines Shannon´s key encryption and the Ford-Fulkerson algorithm, is provided and constitutes a readily implementable secure coding scheme. The derived achievable rate equivocation region is tight when specializing to several special cases. In particular, when the communication network decouples into nonoverlapping parallel paths, the proposed encoding scheme is optimal, i.e., it achieves the secure communication capacity for such networks.